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This circle passes through the points (-1, 2), (3,2) and (9,0). The center of the circle is at (h,k). What is the value of h+k?

 Jul 16, 2022
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Suppose we have a triangle with coordinates (-1, 2), (3, 2), and (9, 0).  The circumcenter which is (h, k) is equidistanct from all the points. From this we can form two equations:

 

(h-3)^2 + (k-2)^2 = (h-9)^2 + k ^2

(h + 1)^2 + (k - 2)^2 = (h - 9)^2 + k^2

 

Simplifying those two equations gives us:
3h - k = 17

5h - k = 19

 

Can you solve h and k from here and find h + k?

 Jul 17, 2022

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